Efficient computation of the wavelet transforms

An efficient algorithm is presented for the computation of the continuous wavelet transform (CWT). CWTs arise in the analysis of bandpass signals that are scale-time perturbed. To detect scale-time perturbed signals, the CWT of the received signal has to be computed with respect to the signals being detected. Efficient algorithms exist for the computation of the discrete wavelet transform, because the DWT wavelets give rise to quadrature mirror filters which can be implemented using lattice structures. Computation of the CWT with respect to an arbitrary wavelet (not necessarily a DWT wavelet), is time consuming. The DWT wavelets are used to compute the CWT of a signal with respect to an arbitrary wavelet. This is accomplished by using the computational properties of compactly supported DWT wavelet bases